The Aftershock uses an internal microphone in order to capture low frequency sounds. Using a circuit board it transfers and amplifies the signal to an electric motor at the opposite end of the light. The motor is rigidly attached via a bracket assembly to a mirror, and contains a weight on its axle to provide uneven interial loading to the assembly. The shake table assembly is then bound in a neoprene diaphragm that allows relatively limited motion of the shake table.

+

The Aftershock uses an internal microphone in order to capture low frequency sounds. Using a circuit board it transfers and amplifies the signal to an electric motor at the opposite end of the light. The motor is rigidly attached via a bracket assembly (see figure 2) to a mirror, and contains a weight on its axle to provide uneven interial loading to the assembly. The shake table assembly is then bound in a neoprene diaphragm that allows relatively limited motion of the shake table.

Every component in the assembly has a life expectancy due wear generated by constant friction and other forces acting on the parts. This expectency varies between individual parts based on the location, direction and magnitude of the forces acting on the part and also the geometery and material compositon of the part.

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−

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For the force requirement on the gears to rotate the grind wheel at 10,000 RPM, the power consumption of the grinder was researched. From the power consumption the torque was calculated to be 0.315 Nm, which equates to about 2.61 lbs of force on the workpeice from the grind wheel. This calculates to 12.4626 N of force at the gears to rotate the grind wheel at 10,000 RPM.

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To calculate the stress in the gears, a stress equation was used from the ''Fundamentals of Machine Components Design'' by Robert C. Juvinall. The velocity factor was caluated with the assumption that the gears were precision shaved and ground. The overload factor was calculated with the assumption that the source of power is uniform and the driven machinery is assumed to have moderate shock. Both gears were overhung, which gave a mounting factor of 1.25. The calculated stress in the smaller gear was 613.601 PSI and the stress in the larger gear was 442.438 PSI.

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To calculate the life of the bearing a life expectancy equation was used from the ''Fundamentals of Machine Components Design'' by Robert C. Juvinall. It was found that common practice was to use a dynamic load for a like of 9X10^6 seconds. Assuming the grinder will be used constantly the bearing will last 3.33*10^7 years before failure. If the grinder will be used six hours every day, 365 days a year then the bearing will last 1.33*10^8 years. Under the more realisitic assumption that the grinder will be used six hours a day, five days a week, the bearing will last 1.86*10^8 years.

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==Parts==

==Parts==

Line 106:

Line 98:

==Engineering Specifications==

==Engineering Specifications==

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The table belows details the Convective Cooling Rate of the Fan:

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The table belows details the convective cooling rate of the fan:

{| border="1" align="center"

{| border="1" align="center"

Line 126:

Line 118:

! 4

! 4

|align="center"|Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

|align="center"|Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

−

| align="center"|A psychrometric analysis of the air being used to cool the system was conducted to determine the amount of heat transfer out of the light via direct convection. The volumetric flow rate of the air was calculated by V= v*A, where V is the volumetric flow rate, v is the velocity of the air at the fan inlet, and A is the cross sectional area of the fan inlet. The enthalpies of the air at the inlet and outlet were found through measurements of air temperature and relative humidity followed by use of the ASME psychrometric chart. The total heat transfer in the air was then determined by multiplying the mass flow rate of air (calculated by m=V/v, where m is the mass flow rate, V is the volumetric flow rate, and v is the specific volume of air at the inlet) by the change in enthalpy between the inlet and outlet per unit mass (Q= m*(houtlet-hinlet)), where Q is the rate of heat transfer, m is the mass flow rate, and h is the enthalpy of the air at various sites). The total heat generated by the bulb was equal to 0.95 times the bulb wattage (incandescent bulbs convert 95% of their input energy into waste heat).

+

| align="center"|A psychrometric analysis of the air being used to cool the system was conducted to determine the amount of heat transfer out of the light via direct convection. The volumetric flow rate of the air was calculated by V= v*A, where V is the volumetric flow rate, v is the velocity of the air at the fan inlet, and A is the cross sectional area of the fan inlet. The enthalpies of the air at the inlet and outlet were found through measurements of air temperature and relative humidity followed by use of the ASME psychrometric chart. The total heat transfer in the air was then determined by multiplying the mass flow rate of air (calculated by m=V/v, where m is the mass flow rate, V is the volumetric flow rate, and v is the specific volume of air at the inlet) by the change in enthalpy between the inlet and outlet per unit mass (Q= m*(h_outlet-h_inlet)), where Q is the rate of heat transfer, m is the mass flow rate, and h is the enthalpy of the air at various sites). The total heat generated by the bulb was equal to 0.95 times the bulb wattage (incandescent bulbs convert 95% of their input energy into waste heat).

|-

|-

! 5

! 5

Line 144:

Line 136:

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The table belows explains the caclation of the force on the gears:

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The table belows describes the maximum angular deflection of the mirror:

| align="center"|Force on the Gears in a tangential direction, the target value is the lowest possible value to achieve 10,000 rpm at the grind wheel, direction of improvement is ↓, the user requirements related are tool life and grinding ability.

+

| align="center"|The maximum angular deflection of the mirror determines the size of the area the lighting effect will cover, as well as the complexity of the light patterns that can be produced. Coverage area and pattern complexity increase with increasing maximum deflection, hence the direction of improvement for this specification is larger maximum deflection. The target value for this specification is 20 degrees from the centerline axis of the governing diaphragm.

|-

|-

! 2

! 2

|align="center"|Design decisions/parameters affected

|align="center"|Design decisions/parameters affected

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| align="center"|Torque required at the motor, type of gears used, design of gears

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| align="center"|The geometry of the shake table will determine the magnitude of the loading on the diaphragm. This in turn will affect the maximum deflection seen in the mirror. The maximum speed of the motor will also have an effect on the deflection of the mirror.

|-

|-

! 3

! 3

|align="center"|Key geometric, inertia, and material properties

|align="center"|Key geometric, inertia, and material properties

−

| align="center"|Gear Ratio (31:9), Strength of gear

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| align="center"|The shape of the shake table and connection point to the diaphragm determines the magnitude of the diaphragm loading. The materials used in the shake table design will affect the moments of inertia for the assembly, and consequently the maximum deflection of the mirror.

|-

|-

! 4

! 4

|align="center"|Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

|align="center"|Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

−

| align="center"|We looked up the power requirement for the grinder using P=IV. Then using P=Tω we found the torque provided by the motor. Knowing the radii of the gears we found the tangential force on the gears.

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| align="center"|A visual analysis of the device was performed under standard operating conditions. A protractor was mounted parallel to the side of the light such that, when the machine was off, the mirror rested at the zero degree mark. The sound sensitivity of the aftershock was placed at its maximum setting and the light was placed next to a 300 W main channel speaker operating at full volume. Observations of the position of the mirror relative to the protractor were then made and recorded.

|-

|-

! 5

! 5

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|align="center"|Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

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|align="center"|Boundary Conditions and Loading

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| align="center"|P=IV (5.5 amps/2)*120V = 330 Watts

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| align="center"|The motion of the mirror is caused by a weight rotating at a variable speed at the base of the shake table assembly. The motion produced as a reaction to this inertial loading is constrained by the diaphragm assembly. The diaphragm is also responsible for connecting the shake table assembly to the frame of the light.

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P=Tω ω = (10,000*2*pi) / 60

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T = 330/ω = 0.315 Nm

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.315/0.05715 = 5.51 kg

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5.51 * 9.81 = 12.4626 N at the gears

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|-

|-

! 6

! 6

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|align="center"|Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

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| align="center"|The displacement observations showed that the aftershock mirror exhibited a maximum angular displacement of 20 degrees. This displacement was subsequently used as a model criterion when the shake table and assembly and diaphragm were modeled in ADAMS. (See Figure 3 for a plot of the Angular Displacement vs. Time).

+

|-

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! 7

|align="center"|What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

|align="center"|What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

−

| align="center"|Lowering the force on the gears would improve this engineering specification. This would allow the motor to be smaller as well as the grinder to be more compact. The draw backs of this is that it decreases RPM’s at the grinder wheel which would decrease the performance of the grinder.

+

| align="center"|An actuator system could be used to control the mirror geometry instead of the weight and diaphragm system. American DJ has produced several lights using this technology, including the Confusion sound sensitive light system. This system is much more prone to damage in harsh environments but can produce far superior lighting patterns, both in terms of lighting area and pattern complexity.

| align="center"|Stress in the gears that could lead to failure, below 100 ksi (yield stress of steel) ↓, the related user requirement is tool life

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| align="center"|The rubber diaphragm that constrains the shake table motion is subject to a repeated, varied, cyclical loading. The diaphragm should be able to withstand 10.8 million loading cycles (at three cycles per second this corresponds to 1000 hours of operating time). The direction of improvement for this specification is an increasing number of load cycles. This specification relates to the durability user requirement.

|-

|-

! 2

! 2

|align="center"|Design decisions/parameters affected

|align="center"|Design decisions/parameters affected

−

| align="center"|Type of material used, gear design

+

| align="center"|The stiffness of the rubber and the size of the diaphragm are both important design considerations. The stiffness of the rubber determines how effectively the diaphragm dampens the motion of the shake table. A stiffer rubber will produce a larger dampening force, allowing for a smaller diaphragm. However, a smaller diaphragm will experience a greater stress, and therefore have a shorter lifetime. Additionally, consideration must be given to the diaphragm geometry. The shape of the diaphragm will govern whether the dampening of the shake table motion is symmetric or not. A circular diaphragm was used to ensure symmetric dampening.

|align="center"|Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

|align="center"|Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

−

| align="center"|σ = (FtP/bJ)KvKoKm where Ft is the tangential load in pounds, P is the diamertral pitch at the large end of the tooth, b is the face width, J is the geometry factor, Kv is the velocity factor Ko is the overload factor and Km is the mounting factor. The velocity factor was caluated with the assumption that the gears were precision shaved and ground. The overload factor was calculated with the assumption that the source of power is uniform and the driven machinery is assumed to have moderate shock. Both gears were overhung, which gave a mounting factor of 1.25.

+

| align="center"|The shake table assembly was modeled in Pro/Engineer and ported into the ADAMS environment for a stress analysis. The diaphragm was modeled as a system of eight grounded springs connected to a massless disc in the shape of the actual diaphragm. All mass and inertial properties of the system were determined in Pro/Engineer and applied in ADAMS. The rotating weight was given an angular velocity of three rotations per second (equal to the maximum angular velocity in real-life operating conditions). The stiffness of the springs was then set such that the angular displacement of the mirror matched the real life operating conditions (angular displacement of approximately 20 degrees from the centerline axis).

+

ADAMS’ postprocessor was then used to determine the maximum force experienced in each spring. This force was found to be approximately 1 Newton. An order of magnitude analysis was then performed to get a rough estimate of maximum lifetime cycles.

|-

|-

! 5

! 5

−

|align="center"|Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

+

|align="center"|Boundary Conditions and Loading

−

| align="center"|From figure 16.13 in the Juvinall book, J for the little gear was found to be 0.2, and J for the big gear was found to be 0.18. Kv was calculated by using the equation (50 + sqrt(v))/50. Calculating a V in ft/min. V=rω, V=10,000(2*pi)(0.075) = 4712.389 ft/min. Ko was found to be 1.25 from table 15.1 in the Juvinall book. Km was found to be 1.25 from table 16.1 in the Juvinall book. P = Np/dp. For the smaller gear, P = 16.216 and for the larger geat P = 17.22. Combining all of this with a force of 12.4626 N or 0.2248 lbs the calculated stress in the smaller gear was 613.601 PSI and the stress in the larger gear was 442.438 PSI.

+

| align="center"|The actual diaphragm consists of two pieces of rubber pressed between steel plates. The plates were designed such that only a 3-in diameter section of the diaphragm could move. The loading the diaphragm experiences is due to gravity and the shake table motion. This loading resulted in a 1 Newton force when modeled in ADAMS. See Figure 4 for Diaphragm geometry.

|-

|-

! 6

! 6

+

|align="center"|Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

+

| align="center"|Equations could not be found to calculate the exact stress experienced by the diaphragm, but the use of s=F/A, where s is stress, F is the force, and A is the area of the diaphragm, predicts the stress to be on the order of 102 Pa. Experimental data from Mars and Fatemi’s paper, Multiaxial Stress Effects on Fatigue Behavior of Filled Natural Rubber, indicates a 50 million cycle lifetime at a stress of 7.5*105 Pa. Given that the stress in the diaphragm is three orders of magnitude smaller it is reasonable to say that failure due to fatigue will not happen. (See figure 5 for a the Force vs. Time plot for one of the springs). The rubber will decay through simple aging far before sufficient cycles would be reached for fatigue failure.

+

|-

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! 7

|align="center"|What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

|align="center"|What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

−

| align="center"|Many changes could be made in the design of the gears to decrease the stress in the gears. For example, P, or the ratio of the number of teeth to the diameter of the teeth could be decreased. This would directly lower the stress in the gears. Another example would be increases the face width of the gears, this would increase the surface for the force on the gears to be transmitted, also directly decreasing the stress in the gears. Also utilizing a different geometry would ultimately change the stress in the gears. The trade-offs would be that most of the examples of how to decrease stress, increase the material needed. This will increase the weight of the gears as well as increase the production cost.

+

| align="center"|The diaphragm size and rubber stiffness could be changed, allowing for different diaphragm geometries. However, it makes no sense to change the diaphragm given the robust nature of the design in resisting cyclic failure. The diaphragm is extremely well suited to this particular application.

Latest revision as of 00:49, 26 March 2007

Contents

Description

The main purpose of the Aftershock is to provide beat sensitive party lighting that is capable of sufficiently lighting up a party space. The purpose of this wiki is to provide insight into the internal workings of the light.

How It Works

The Aftershock uses an internal microphone in order to capture low frequency sounds. Using a circuit board it transfers and amplifies the signal to an electric motor at the opposite end of the light. The motor is rigidly attached via a bracket assembly (see figure 2) to a mirror, and contains a weight on its axle to provide uneven interial loading to the assembly. The shake table assembly is then bound in a neoprene diaphragm that allows relatively limited motion of the shake table.

Figure 2: Bracket Assembly

Parts

The table belows lists the Bill of Materials for the American DJ Aftershock:

Table 1: American DJ Aftershock Bill of Materials

Part #

Part Name

# Category

Function

Material

Picture

1

Grounded AC Power Supply

Input

Allows the light to be powered off of a standard wall outlet

Plastic casing with steel and copper prongs

2

Transformer

Input

Changes the AC power input to DC power

Copper wiring used for coils

3

Internal Microphone

Input

Differentiates low frequencies sounds

Steel with a rubber housing

4

Geared Motor

Output

Rotates the reflector

Steel gears

5

Shake Table Motor with Added Destabilizing Weight

Output

Allows for the motor to spin unevenly since the distribution of weight is lopsided

Steel nuts, weight and screw

6

Fan with Motor

Output

Cool the inside of the light and prevent overheating

Steel casing and fan blades

7

Diaphragm

Structural Components

Holds shake table and weighted motor in place

Steel plates, nuts and screws

Rubber or neoprene for the diaphragm

8

Reflector

Other

Rotates on the geared motor and the light hits the various reflective mirrors on the lens

A fan is used to circulate air through the apparatus and cool the bulb. How much direct heat removal through the air (not convection/conduction/convection through the casing) is necessary for steady-state operation? The more heat that can be removed via air cooling the lower the steady state temperature inside the apparatus will be resulting in longer operating times. Therefore, the direction of improvement for this specification is increasing the convective heat transfer. The target value is a minimum of one quarter (25%) of the total heat output being removed via air cooling. This specification relates to the safety user requirement.

2

Design decisions/parameters affected

Higher fan speeds, and therefore higher air flow rates, involve more expensive equipment, higher power requirements, more noise and larger forces. A balance must be struck between these considerations and the ultimate goal of heat removal. This decision will affect the maximum temperature experienced in the light, the lifetime of the circuitry, and the maximum runtime of the light without overheating.

3

Key geometric, inertia, and material properties

Fan speed, inlet size, outlet size, inlet and outlet placement

4

Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

A psychrometric analysis of the air being used to cool the system was conducted to determine the amount of heat transfer out of the light via direct convection. The volumetric flow rate of the air was calculated by V= v*A, where V is the volumetric flow rate, v is the velocity of the air at the fan inlet, and A is the cross sectional area of the fan inlet. The enthalpies of the air at the inlet and outlet were found through measurements of air temperature and relative humidity followed by use of the ASME psychrometric chart. The total heat transfer in the air was then determined by multiplying the mass flow rate of air (calculated by m=V/v, where m is the mass flow rate, V is the volumetric flow rate, and v is the specific volume of air at the inlet) by the change in enthalpy between the inlet and outlet per unit mass (Q= m*(h_outlet-h_inlet)), where Q is the rate of heat transfer, m is the mass flow rate, and h is the enthalpy of the air at various sites). The total heat generated by the bulb was equal to 0.95 times the bulb wattage (incandescent bulbs convert 95% of their input energy into waste heat).

5

Boundary Conditions and Loading

No significant mechanical stresses were placed on the system in this analysis. The light bulb presented a thermal load of 380W.

6

Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

Experimental observations of the aftershock under steady-state operating conditions showed the inlet velocity to be 2.55 m/s (Inlet diameter was 10.16 cm). The inlet temperature was 20.8oC with a relative humidity of 34.7 %; this led to an inlet enthalpy of 35 kJ/kg. The outlet temperature was 24.8oC with a relative humidity of 26.7 %; these conditions specify an outlet enthalpy of 39.5 kJ/kg. Once all data was calculated as described above it was found that the convective heat transfer out of the system via air cooling was approximately 112 W. This represents approximately 29.4% of the total thermal load of the system. Therefore, the remaining 268 W of thermal loading are being dissipated through the metal casing of the system.

7

What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

The use of a higher fan speed would allow for a higher mass flow rate of air through the system. This would result in a higher amount of convective heat transfer out of the light, and therefore a lower operating temperature. However, given that the light can already run uninterrupted for hours at a time the costs associated with installing a more powerful fan likely do not make it a worthwhile investment.

The table belows describes the maximum angular deflection of the mirror:

The maximum angular deflection of the mirror determines the size of the area the lighting effect will cover, as well as the complexity of the light patterns that can be produced. Coverage area and pattern complexity increase with increasing maximum deflection, hence the direction of improvement for this specification is larger maximum deflection. The target value for this specification is 20 degrees from the centerline axis of the governing diaphragm.

2

Design decisions/parameters affected

The geometry of the shake table will determine the magnitude of the loading on the diaphragm. This in turn will affect the maximum deflection seen in the mirror. The maximum speed of the motor will also have an effect on the deflection of the mirror.

3

Key geometric, inertia, and material properties

The shape of the shake table and connection point to the diaphragm determines the magnitude of the diaphragm loading. The materials used in the shake table design will affect the moments of inertia for the assembly, and consequently the maximum deflection of the mirror.

4

Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

A visual analysis of the device was performed under standard operating conditions. A protractor was mounted parallel to the side of the light such that, when the machine was off, the mirror rested at the zero degree mark. The sound sensitivity of the aftershock was placed at its maximum setting and the light was placed next to a 300 W main channel speaker operating at full volume. Observations of the position of the mirror relative to the protractor were then made and recorded.

5

Boundary Conditions and Loading

The motion of the mirror is caused by a weight rotating at a variable speed at the base of the shake table assembly. The motion produced as a reaction to this inertial loading is constrained by the diaphragm assembly. The diaphragm is also responsible for connecting the shake table assembly to the frame of the light.

6

Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

The displacement observations showed that the aftershock mirror exhibited a maximum angular displacement of 20 degrees. This displacement was subsequently used as a model criterion when the shake table and assembly and diaphragm were modeled in ADAMS. (See Figure 3 for a plot of the Angular Displacement vs. Time).

7

What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

An actuator system could be used to control the mirror geometry instead of the weight and diaphragm system. American DJ has produced several lights using this technology, including the Confusion sound sensitive light system. This system is much more prone to damage in harsh environments but can produce far superior lighting patterns, both in terms of lighting area and pattern complexity.

The rubber diaphragm that constrains the shake table motion is subject to a repeated, varied, cyclical loading. The diaphragm should be able to withstand 10.8 million loading cycles (at three cycles per second this corresponds to 1000 hours of operating time). The direction of improvement for this specification is an increasing number of load cycles. This specification relates to the durability user requirement.

2

Design decisions/parameters affected

The stiffness of the rubber and the size of the diaphragm are both important design considerations. The stiffness of the rubber determines how effectively the diaphragm dampens the motion of the shake table. A stiffer rubber will produce a larger dampening force, allowing for a smaller diaphragm. However, a smaller diaphragm will experience a greater stress, and therefore have a shorter lifetime. Additionally, consideration must be given to the diaphragm geometry. The shape of the diaphragm will govern whether the dampening of the shake table motion is symmetric or not. A circular diaphragm was used to ensure symmetric dampening.

3

Key geometric, inertia, and material properties

Rubber type, modulus of elasticity, diaphragm shape, diaphragm size

4

Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions

The shake table assembly was modeled in Pro/Engineer and ported into the ADAMS environment for a stress analysis. The diaphragm was modeled as a system of eight grounded springs connected to a massless disc in the shape of the actual diaphragm. All mass and inertial properties of the system were determined in Pro/Engineer and applied in ADAMS. The rotating weight was given an angular velocity of three rotations per second (equal to the maximum angular velocity in real-life operating conditions). The stiffness of the springs was then set such that the angular displacement of the mirror matched the real life operating conditions (angular displacement of approximately 20 degrees from the centerline axis).

ADAMS’ postprocessor was then used to determine the maximum force experienced in each spring. This force was found to be approximately 1 Newton. An order of magnitude analysis was then performed to get a rough estimate of maximum lifetime cycles.

5

Boundary Conditions and Loading

The actual diaphragm consists of two pieces of rubber pressed between steel plates. The plates were designed such that only a 3-in diameter section of the diaphragm could move. The loading the diaphragm experiences is due to gravity and the shake table motion. This loading resulted in a 1 Newton force when modeled in ADAMS. See Figure 4 for Diaphragm geometry.

6

Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?

Equations could not be found to calculate the exact stress experienced by the diaphragm, but the use of s=F/A, where s is stress, F is the force, and A is the area of the diaphragm, predicts the stress to be on the order of 102 Pa. Experimental data from Mars and Fatemi’s paper, Multiaxial Stress Effects on Fatigue Behavior of Filled Natural Rubber, indicates a 50 million cycle lifetime at a stress of 7.5*105 Pa. Given that the stress in the diaphragm is three orders of magnitude smaller it is reasonable to say that failure due to fatigue will not happen. (See figure 5 for a the Force vs. Time plot for one of the springs). The rubber will decay through simple aging far before sufficient cycles would be reached for fatigue failure.

7

What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?

The diaphragm size and rubber stiffness could be changed, allowing for different diaphragm geometries. However, it makes no sense to change the diaphragm given the robust nature of the design in resisting cyclic failure. The diaphragm is extremely well suited to this particular application.